268 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
4—7—n (4—2 1) —2 vii tt 
. n 
which is satisfied by »=3 and n=1. 
Th 8: 
Hence ee ere 
Cor. 2. If be a whole number 7; /n=1.2...(r—1) 
and /n+$=4.3...(7—) Jv 

12 tea a1 oe ee eee 
will determine the integral values of 7. 

If n=r+k, |n =t3 Or va, jos 28 or 
and BeBe OPO fir Va 1.2.2 pb OED ee 26 

which determines the fractional values of x which have 2 as their denominator. 
Now it is evident that these are the only forms which n can assume; there- 
fore the determination of the values of 7 is reduced to the solution of these two 





equations. 
Ex. 4. yravel 4s bn St x. 
Let X36 ce . then 
y=da,e "+36, (1+4 Vestn — one 
wae —nb is La ia ad a 
(he Ves [r+1 
the values of n being determined as in Example 3. 
Cor. If r=p, n=p, we obtain, as in other instances, 





ay, log x ae aa 
=> —+ C +2 ————— : 
g ar P g SS isae /s+1 
Vea 2 5 | 
/s /s . 
h C : | 
where = — 
ae 7 | i 
aV=ig Pts —6b 
|p 
Ex. 
Or 
